Weighted Bergman Kernels and Quantization}

Let Ω be a bounded pseudoconvex domain in C ^N , φ, ψ two positive functions on Ω such that − log ψ, − log φ are plurisubharmonic, and z∈Ω a point at which − log φ is smooth and strictly plurisubharmonic. We show that as k→∞, the Bergman kernels with respect to the weights φ ^{k ψ} have an asymptotic expansion

Covariant Perturbation Expansion of Off-Diagonal Heat Kernel

Covariant perturbation expansion is an important method in quantum field theory. In this paper an expansion up to arbitrary order for off-diagonal heat kernels in flat space based on the covariant perturbation expansion is given. In literature, only diagonal heat kernels are calculated based on the covariant perturbation expansion.     

Crystal Melting and Toric Calabi-Yau Manifolds

We construct a statistical model of crystal melting to count BPS bound states of D0 and D2 branes on a single D6 brane wrapping an arbitrary toric Calabi-Yau threefold. The three-dimensional crystalline structure is determined by the quiver diagram and the brane tiling which characterize the low energy effective theory of D branes. The crystal is composed of atoms of different colors, each of which corresponds to a node of the quiver diagram, and the chemical bond is dictated by the arrows of the quiver diagram. BPS states are constructed by removing atoms from the crystal. This generalizes the earlier results on the BPS state counting to an arbitrary non-compact toric Calabi-Yau manifold. We point out that a proper understanding of the relation between the topological string theory and the crystal melting involves the wall crossing in the Donaldson-Thomas theory.     

The Nekrasov Conjecture for Toric Surfaces

The Nekrasov conjecture predicts a relation between the partition function for N = 2 supersymmetric Yang–Mills theory and the Seiberg-Witten prepotential. For instantons on \mathbbR⁴{\mathbb{R}^4}, the conjecture was proved, independently and using different methods, by Nekrasov-Okounkov and Nakajima-Yoshioka. We prove a generalized version of the conjecture for instantons on noncompact toric surfaces.     

Toric Self-Dual Einstein Metrics as Quotients

We use the quaternion Kähler reduction technique to study old and new self-dual Einstein metrics of negative scalar curvature with at least a two-dimensional isometry group, and relate the quotient construction to the hyperbolic eigenfunction Ansatz. We focus in particular on the (semi-)quaternion Kähler quotients of (semi-)quaternion Kähler hyperboloids, analysing the completeness and topology, and relating them to the self-dual Einstein Hermitian metrics of Apostolov–Gauduchon and Bryant.During the preparation of this work the first and third authors were supported by NSF grant DMS-0203219. The second author was supported by the Leverhulme Trust, the William Gordon Seggie Brown Trust and an EPSRC Advanced Fellowship. The fourth author was supported by the MIUR Project Proprietà Geometriche delle Varietà Reali e Complesse. The authors are also grateful for support from EDGE, Research Training Network HPRN-CT-2000-00101, funded by the European Human Potential Programme.Acknowledgement The first author thanks the Ecole Polytechnique, Palaiseau and the Università di Roma La Sapienza for hospitality and support. The third author would like to thank the Università di Roma La Sapienza, I.N.d.A.M, M.P.I-Bonn, and IHES as parts of this paper were written during his visits there. The fourth named author would like to thank University of New Mexico for hospitality and support. The authors are grateful to Paul Gauduchon, Michael Singer and Pavel Winternitz for invaluable discussions.     

On-Diagonal Estimates on Schrödinger Semigroup Kernels and Reduced Heat Kernels

We prove various estimates for the kernels of semigroups generated by Schr?dinger operators with magnetic field and potential of polynomial growth. We also investigate the reduced heat kernels. Received: 25 May 1996 / Accepted: 29 January 1997     

Uniqueness and Examples of Compact Toric Sasaki-Einstein Metrics

In [11] it was proved that, given a compact toric Sasaki manifold with positive basic first Chern class and trivial first Chern class of the contact bundle, one can find a deformed Sasaki structure on which a Sasaki-Einstein metric exists. In the present paper we first prove the uniqueness of such Einstein metrics on compact toric Sasaki manifolds modulo the action of the identity component of the automorphism group for the transverse holomorphic structure, and secondly remark that the result of [11] implies the existence of compatible Einstein metrics on all compact Sasaki manifolds obtained from the toric diagrams with any height, or equivalently on all compact toric Sasaki manifolds whose cones have flat canonical bundle. We further show that there exists an infinite family of inequivalent toric Sasaki-Einstein metrics on for each positive integer k.     

Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds

We present a proof of the mirror conjecture of Aganagic and Vafa (Mirror Symmetry, D-Branes and Counting Holomorphic Discs. http://arxiv.org/abs/hep-th/0012041v1, 2000) and Aganagic et al. (Z Naturforsch A 57(1–2):128, 2002) on disk enumeration in toric Calabi-Yau 3-folds for all smooth semi-projective toric Calabi-Yau 3-folds. We consider both inner and outer branes, at arbitrary framing. In particular, we recover previous results on the conjecture for (i) an inner brane at zero framing in ${K_{\mathbb{P}^2}}$ K P 2 (Graber-Zaslow, Contemp Math 310:107–121, 2002), (ii) an outer brane at arbitrary framing in the resolved conifold ${\mathcal{O}_{\mathbb{P}^1}(-1)\oplus \mathcal{O}_{\mathbb{P}^1}(-1)}$ O P 1 ( - 1 ) ⊕ O P 1 ( - 1 ) (Zhou, Open string invariants and mirror curve of the resolved conifold. http://arxiv.org/abs/1001.0447v1 [math.AG], 2010), and (iii) an outer brane at zero framing in ${K_{\mathbb{P}^2}}$ K P 2 (Brini, Open topological strings and integrable hierarchies: Remodeling the A-model. http://arxiv.org/abs/1102.0281 [hep-th], 2011).     

Decay of hypernuclei

We present a nonrelativistic transition potential for the weak strangeness-changing reaction ΛN → NN. The potential is based on a one meson exchange model (OME), where, in addition to the long-ranged pion, the exchange of the pseudoscalar K, η, as well as the vector ,ω, K^* mesons is considered. Results obtained for different hypernuclear decay observables are compared to the available experimental data.     

Bergman Kernel from Path Integral

We rederive the expansion of the Bergman kernel on Kähler manifolds developed by Tian, Yau, Zelditch, Lu and Catlin, using path integral and perturbation theory, and generalize it to supersymmetric quantum mechanics. One physics interpretation of this result is as an expansion of the projector of wave functions on the lowest Landau level, in the special case that the magnetic field is proportional to the Kähler form. This is relevant for the quantum Hall effect in curved space, and for its higher dimensional generalizations. Other applications include the theory of coherent states, the study of balanced metrics, noncommutative field theory, and a conjecture on metrics in black hole backgrounds discussed in [24]. We give a short overview of these various topics. From a conceptual point of view, this expansion is noteworthy as it is a geometric expansion, somewhat similar to the DeWitt-Seeley-Gilkey et al short time expansion for the heat kernel, but in this case describing the long time limit, without depending on supersymmetry.     

Interplay of Kitaev Interaction and Off-Diagonal Exchanges: Exotic Phases and Quantum Phase Diagrams

<正>Aligning with the ongoing search for quantum spin liquids(QSLs), identifying QSLs in Kitaev magnets has attracted significant research interest during the past decade. Nevertheless, it remains a significant challenge.One of the major difficulties is that Kitaev QSL is typically fragile to competing interactions such as off-diagonal exchanges, which are ubiquitous in real materials owing to spin-orbit coupling and crystal-field effects.     

Decay of Hf172

The internal conversion spectrum of Hf¹⁷² was examined with an intermediate image magnetic spectrometer. The gamma-ray spectrum and gamma-gamma coincidence spectrum were studied by means of scintillation spectrometers. The half-life of the 65·9 keV excited level in Lu¹⁷² was found to beT _1/2 = (3·32±0·20) × 10^–7 sec. The proposed decay scheme is discussed.On the same apparatus the half-life of the 206·25 keV excited level in Re¹⁸⁷ was measured and the result isT _1/2 = (5·05±0·13) × 10^–7 sec.The authors wish to thank to Ing. Vobecký and Ing. Matalka for the separation of Hf and Z. Praáková for assistance in the numerical calculation.     

Decay of 143Sm

The decay of ¹⁴³Sm has been investigated by means of a Ge(Li) spectrometer. Levels of ¹⁴³Pm at 272.9, 1056.6, 1173.3, 1341.0, 1403.5, 1515.7, 1751.3, 1816.8, 2009.6, 2081.2 and 2172.5 keV have been established. Gamma-gamma coincidences confirmed the existence of the 272.9 keV level. Spin and parity assignments for all observed levels have been suggested from electron capture and positon disintegration considerations and gamma branches. The level is compared with an extreme one-quasi-particle model and an extended one-plus-three-quasi-particle Tamm-Dancoff approximation.     

Decay properties of baryonia

Decay properties of baryonia are discussed and widths are estimated for L = 1 states. All presently known candidates for baryonia are shown to have properties consistent with those expected. Several novel characteristics which are to be anticipated are pointed out.     

Decay of78Br

The decay of⁷⁸Br was investigated with a Ge(Li) spectrometer and Ge(Li)-NaI(Tl) coincidence methods. Accurate energy and intensity determinations of 14 gamma rays have been performed. A level scheme with levels at 614.0, 1,308.1, 1,498.4, 1,758.5, 1,993.7, 2,334.4, 2,538, 3,090 and 3,253 keV is deduced. Spin and parity indications for most of the observed levels are given from electron capture and positon decay considerations and gamma branches.     

Decay of Hoyle state

The prediction of Hoyle state was necessitated to explain the abundance of carbon, which is crucial for the existence of life on Earth and is the stepping stone for understanding the abundance of other heavier elements. After the experimental confirmation of its existence, soon it was realized that the Hoyle state was ‘different’ from other excited states of carbon, led to intense theoretical and experimental activities over the past few decades to understand its structure. In recent times, precision, high statistics experiments on the decay of Hoyle state have been performed at the Variable Energy Cyclotron Centre, to determine the quantitative contributions of various direct 3 α decay mechanisms of the Hoyle state. The present results have been critically compared with those obtained in other recent experiments and their implications have been discussed.     

Decay of63Zn

Investigation of the 38.8 min decay of⁶³Zn has resulted in 31 gamma-ray transitions in⁶³Cu. New levels not earlier reported inΒ ⁺-decay of⁶³Zn, but found in nuclear reactions, are suggested at 2,010.9 and 3,101 keV. It is assumed that the excited core model generates a multiplet of levels at 669.75 keV (1/2^?), 962.1 keV (5/2^?), 1,327.1 keV (7/2^?) and 1,546.6 keV (3/2^?). Intensities for intramultiplet transitions were found to be: 219.4 keV, <0.004 (in units of 200 for annihilation radiation), 292.4 keV, <0.004, 365.0 keV, 0.03±0.03, 584.4 keV, <0.005, and 876.8 keV, <0.005.